Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#442 ⋊ C2 |
| Sylow | C43 ⋊ #3264 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#442 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #442 | D43 |
| hypocenter | C43 | #3264 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
568 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^42,d^b=de,e^b=eg,h^c=h^42,e^d=eg491 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#3264, C2×#19146077, #25971670, … |
| maximal normal subgroup of | D43×#3264, C2×#19146077, #25971670, … |
| maximal quotient of | #25085946, #25086066, #25086186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 15992);